{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:EMRH6WBZ5E3IGXN72HB3G52MTJ","short_pith_number":"pith:EMRH6WBZ","canonical_record":{"source":{"id":"2212.01664","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-12-03T18:35:05Z","cross_cats_sorted":["math.DG","math.SG"],"title_canon_sha256":"eb7938b49a1a78450ef6b3cb2177857f20669b7a18932adfbf3ce2c4a0a306d8","abstract_canon_sha256":"1ed217ac2ad525e70048234e84f89b820be41b575789df0624e51048430a649b"},"schema_version":"1.0"},"canonical_sha256":"23227f5839e936835dbfd1c3b3774c9a778c8affd276dccc9fc26078aef63309","source":{"kind":"arxiv","id":"2212.01664","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.01664","created_at":"2026-07-05T06:43:46Z"},{"alias_kind":"arxiv_version","alias_value":"2212.01664v2","created_at":"2026-07-05T06:43:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.01664","created_at":"2026-07-05T06:43:46Z"},{"alias_kind":"pith_short_12","alias_value":"EMRH6WBZ5E3I","created_at":"2026-07-05T06:43:46Z"},{"alias_kind":"pith_short_16","alias_value":"EMRH6WBZ5E3IGXN7","created_at":"2026-07-05T06:43:46Z"},{"alias_kind":"pith_short_8","alias_value":"EMRH6WBZ","created_at":"2026-07-05T06:43:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:EMRH6WBZ5E3IGXN72HB3G52MTJ","target":"record","payload":{"canonical_record":{"source":{"id":"2212.01664","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-12-03T18:35:05Z","cross_cats_sorted":["math.DG","math.SG"],"title_canon_sha256":"eb7938b49a1a78450ef6b3cb2177857f20669b7a18932adfbf3ce2c4a0a306d8","abstract_canon_sha256":"1ed217ac2ad525e70048234e84f89b820be41b575789df0624e51048430a649b"},"schema_version":"1.0"},"canonical_sha256":"23227f5839e936835dbfd1c3b3774c9a778c8affd276dccc9fc26078aef63309","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:43:46.362442Z","signature_b64":"RoX9zmreZ+qCM7Q0NF3aqYhToxKahCW2fx953lS2ZVjd5kEYc50/beqHPMTrJY+b6O5Qv5kDx8+NSBk3Ox+cAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23227f5839e936835dbfd1c3b3774c9a778c8affd276dccc9fc26078aef63309","last_reissued_at":"2026-07-05T06:43:46.361983Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:43:46.361983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2212.01664","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:43:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"992gfkOVNKfi716w1pnnx/JBN/YPBl/KVuzo8bgR4ukor1OjLVP/8CgRlNnIQyLXY8mQ6Gqmma5adXZen6xDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T10:04:25.218807Z"},"content_sha256":"f61d7fcc8775453b5111949375c4776d80c516dd8189542b1c04f3023c679bab","schema_version":"1.0","event_id":"sha256:f61d7fcc8775453b5111949375c4776d80c516dd8189542b1c04f3023c679bab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:EMRH6WBZ5E3IGXN72HB3G52MTJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counting rational curves with an $m$-fold point","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG","math.SG"],"primary_cat":"math.AG","authors_text":"Anantadulal Paul, Apratim Choudhury, Chitrabhanu Chaudhuri, Indranil Biswas, Ritwik Mukherjee","submitted_at":"2022-12-03T18:35:05Z","abstract_excerpt":"We obtain a recursive formula for the number of rational degree $d$ curves in $\\mathbb{CP}^2$ that pass through $3d+1-m$ generic points and that have an $m$-fold singular point. The special case of counting curves with a triple point was solved earlier by other authors. We obtain the formula by considering a family version of Kontsevich's recursion formula, in contrast to the excess intersection theoretic approach of others. A large number of low degree cases have been worked out explicitly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.01664","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.01664/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:43:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mW5FpwZ0kUb92IdKsBnxZaE404sLTiAL4BYDNUCbeUKADKV/siDxWhFrRcbhdEqmz04KjbfufiQ9NLPJ2X1cDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T10:04:25.219298Z"},"content_sha256":"6a6ee1c085dd5a825ec87a7076fd028ea989a16298d221b0263f1fd68f03145f","schema_version":"1.0","event_id":"sha256:6a6ee1c085dd5a825ec87a7076fd028ea989a16298d221b0263f1fd68f03145f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EMRH6WBZ5E3IGXN72HB3G52MTJ/bundle.json","state_url":"https://pith.science/pith/EMRH6WBZ5E3IGXN72HB3G52MTJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EMRH6WBZ5E3IGXN72HB3G52MTJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-04T10:04:25Z","links":{"resolver":"https://pith.science/pith/EMRH6WBZ5E3IGXN72HB3G52MTJ","bundle":"https://pith.science/pith/EMRH6WBZ5E3IGXN72HB3G52MTJ/bundle.json","state":"https://pith.science/pith/EMRH6WBZ5E3IGXN72HB3G52MTJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EMRH6WBZ5E3IGXN72HB3G52MTJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:EMRH6WBZ5E3IGXN72HB3G52MTJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1ed217ac2ad525e70048234e84f89b820be41b575789df0624e51048430a649b","cross_cats_sorted":["math.DG","math.SG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-12-03T18:35:05Z","title_canon_sha256":"eb7938b49a1a78450ef6b3cb2177857f20669b7a18932adfbf3ce2c4a0a306d8"},"schema_version":"1.0","source":{"id":"2212.01664","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.01664","created_at":"2026-07-05T06:43:46Z"},{"alias_kind":"arxiv_version","alias_value":"2212.01664v2","created_at":"2026-07-05T06:43:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.01664","created_at":"2026-07-05T06:43:46Z"},{"alias_kind":"pith_short_12","alias_value":"EMRH6WBZ5E3I","created_at":"2026-07-05T06:43:46Z"},{"alias_kind":"pith_short_16","alias_value":"EMRH6WBZ5E3IGXN7","created_at":"2026-07-05T06:43:46Z"},{"alias_kind":"pith_short_8","alias_value":"EMRH6WBZ","created_at":"2026-07-05T06:43:46Z"}],"graph_snapshots":[{"event_id":"sha256:6a6ee1c085dd5a825ec87a7076fd028ea989a16298d221b0263f1fd68f03145f","target":"graph","created_at":"2026-07-05T06:43:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2212.01664/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We obtain a recursive formula for the number of rational degree $d$ curves in $\\mathbb{CP}^2$ that pass through $3d+1-m$ generic points and that have an $m$-fold singular point. The special case of counting curves with a triple point was solved earlier by other authors. We obtain the formula by considering a family version of Kontsevich's recursion formula, in contrast to the excess intersection theoretic approach of others. A large number of low degree cases have been worked out explicitly.","authors_text":"Anantadulal Paul, Apratim Choudhury, Chitrabhanu Chaudhuri, Indranil Biswas, Ritwik Mukherjee","cross_cats":["math.DG","math.SG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-12-03T18:35:05Z","title":"Counting rational curves with an $m$-fold point"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.01664","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f61d7fcc8775453b5111949375c4776d80c516dd8189542b1c04f3023c679bab","target":"record","created_at":"2026-07-05T06:43:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1ed217ac2ad525e70048234e84f89b820be41b575789df0624e51048430a649b","cross_cats_sorted":["math.DG","math.SG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-12-03T18:35:05Z","title_canon_sha256":"eb7938b49a1a78450ef6b3cb2177857f20669b7a18932adfbf3ce2c4a0a306d8"},"schema_version":"1.0","source":{"id":"2212.01664","kind":"arxiv","version":2}},"canonical_sha256":"23227f5839e936835dbfd1c3b3774c9a778c8affd276dccc9fc26078aef63309","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23227f5839e936835dbfd1c3b3774c9a778c8affd276dccc9fc26078aef63309","first_computed_at":"2026-07-05T06:43:46.361983Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:43:46.361983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RoX9zmreZ+qCM7Q0NF3aqYhToxKahCW2fx953lS2ZVjd5kEYc50/beqHPMTrJY+b6O5Qv5kDx8+NSBk3Ox+cAA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:43:46.362442Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.01664","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f61d7fcc8775453b5111949375c4776d80c516dd8189542b1c04f3023c679bab","sha256:6a6ee1c085dd5a825ec87a7076fd028ea989a16298d221b0263f1fd68f03145f"],"state_sha256":"6bd2e184ed8deca23f2e8fab5d33f705b3912b76ace3d0ba1bef783609ff5325"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vOdVZSyD2xlzPVihvToI0nwj0Q0n1qYtfVtLJyrfRuKbdT/5wgwpeZ6MfBRglwY8jGKikgQBaXHGuPTYeBVjBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T10:04:25.223050Z","bundle_sha256":"357f55d8e27b4ed0b3d05bf2cfcbf3e979b7945a1244d1fb3a141930a60cdc38"}}